DISCRETE COSINE TRANSFORM

This chapter presents discrete cosine transform, a real arithmetic and recursive algorithm, developed by Chen, Smith, and Fralick in 1977, was the major breakthrough in the efficient implementation of the DCT.

Abstract

This chapter presents discrete cosine transform. The development of fast algorithms for efficient implementation of the discrete Fourier transform (DFT) by Cooley and Tukey in 1965 has led to phenomenal growth in its applications in digital signal processing (DSP). The discovery of the discrete cosine transform (DCT) in 1974 has provided a significant impact in the DSP field. While the original DCT algorithm is based on the FFT, a real arithmetic and recursive algorithm, developed by Chen, Smith, and Fralick in 1977, was the major breakthrough in the efficient implementation of the DCT. A less well-known but equally efficient algorithm was developed by Corrington. Subsequently, other algorithms, such as the decimation-in-time (DIT),decimation-in-frequency (DIF), split radix, DCT via other discrete transforms such as the discrete Hartley transform (DHT) or the Walsh-Hadamard transform (WHT), prime factor algorithm (PFA), a fast recursive algorithm, and planar rotations, which concentrate on reducing the computational complexity and/or improving the structural simplicity, have been developed. The dramatic development of DCT-based DSP is by no means an accident.